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Upsilon Polarization: at odds with NRQCD August 5, 2007

Posted by dorigo in news, physics, science.

The summer is in full swing, and summer conferences are blossoming all over the place. That means that the CDF and D0 experiments are quite busy approving brand new results on all the most interesting physics measurements and searches, recently obtained with up to two-inverse femtobarn datasets of proton-antiproton collisions provided by the Tevatron collider. Two inverse femtobarns means a whole lot of them: 160,000 billion collisions took place in each detector, and a few billions were written to tape and analyzed.

I am not going to sit here and watch a stream of star new results being published, presented, and consumed without offering my two cents on those that trigger my interest, of course. Unfortunately, I am again going to discuss a new result by D0 today, after two more in the past few days. The fact is, I belong to CDF and have agreed to allow my peers to present their analyses at conferences before discussing them in my blog. So the CDF stuff will be broadcast here with some delay… As for D0, I have no commitment preventing me from discussing their public results, although of course I would like to avoid doing anything they may not like. But the material is public, and this is the internet, baby…

Anyway. The exciting new result by D0 I discuss today is something that arises my interest for at least a couple of different reasons. Make it three.

First, it is about Upsilon mesons – fascinating systems composed of two b-quarks orbiting around each other. I have always had a weak spot for these particles, which were the source of the discovery of the fifth quark by Lederman and colleagues in 1977. There is a whole family of these states, at increasing masses: the Y(1S), Y(2S), Y(3S), Y(4S)… Only the first three of these live long enough to make a narrow resonance when they decay into pairs of muons. The fourth is massive enough to decay to two B hadrons, and in fact low energy electron-positron colliders have exploited the Y(4S) decay to provide a huge amount of B particles. The PEP-II and Kek B-factories have enabled their experiments BaBar and Belle to produce exquisite physics measurements by running “at the Y(4S)”: by adjusting beam energies and crossing angles, these machines can achieve electron-positron collisions with a total center-of-mass energy equal to the mass of the Y(4S) – 10.55 GeV, which maximizes the probability to create that bound state.

Below is a picture worth a thousand words: the invariant mass distribution of pairs of muons reconstructed by CDF in Run 1, showing not just the three narrow. lowest-energy Y states, but also, at far smaller masses, the J/psi and the Psi(2S) – quite similar states composed of two charmed quarks. If you have studied quantum mechanics deep enough to understand bound systems, you cannot help seeing the beauty of this spectrum. The states are called “quarkonium”, underlining the fact that they are not conceptually different from a new state of matter – elemental, in a way, no less than polonium or americium – but actually much closer to positronium, the bound state of an electron-positron pair.

Second (yes, we are still in a list), the result is about Upsilon polarization, and it is a stringent test of NRQCD (non-relativistic quantum chromodynamics). The theory is successful in describing the phenomenology of production and decay of states such as (c \bar c) or (b \bar b) quarkonium. NRQCD basically works by factoring out effects that depend on the dynamics of the quarks in the meson, which are “non-relativistic” in the sense that they typically move at a few tenths of the speed of light inside the bound state. I studied the matter in some detail years ago, when I searched for a very rare process including Y mesons. Although I since forgot most of it, the physics of quarkonium production has remained a dear topic to me. In particular, the polarization (that is, the angle between the spin of the meson and its direction of flight) is a very intriguing and complex property to study, a property of particles which often puts theories to the test.

Third, and most important: the new measurement by D0 is totally at odds with NRQCD. Not just that: it is also in disagreement with the previous CDF measurement of the same quantity. How’s that for a motivation to read further ?

Indeed, there is not too much to describe about the measurement, which is rather straightforward: a large sample of dimuon decays of the Y mesons is collected by D0 from muon triggered data by applying standard identification cuts to muon candidates, and 420,000 Y decays are isolated in a sample of 1.3 inverse femtobarns. Then they define a variable sensitive to the Y polarization – the angle \theta^* which the positive decay muon makes with the direction of flight of the Y, in the center of mass of the decaying body. Finally, the data is divided into many subsets depending on the value of Y transverse momentum P_T^\Upsilon and \cos \theta^* (we say that the data is “binned” to describe the slicing and dicing), and for each subset the number of Y(1S), Y(2S), and Y(3S) events is obtained by a fit to the dimuon mass distribution.

The fit is actually not too easy to perform, since the reconstructed invariant mass of pairs of muons in D0 shows a resolution not too simple to model. D0 parametrizes the mass distribution of each Y state with a function which is the sum of two gaussians (the sum of three gaussians is also tried) – so the three Y(1S), Y(2S), and Y(3S) peaks are understood as the sum of three double (or triple) gaussians, as in the plot shown below, which shows the Y candidates for a narrow bin in \cos \theta^* and Y transverse momentum.

The result of the many fits is the number of Y candidates as a function of the two variables used to bin the data: a differential measurement telling how probable it is for a Y to be produced with a given value of P_T^\Upsilon and \cos \theta^*. These distributions are the starting point of the polarization measurement. If one defines the variable \alpha = (\sigma_T - 2 \sigma_L)/(\sigma_T + 2 \sigma_L), where \sigma_T (\sigma_L) are the transverse and longitudinal polarization components of the total cross section, then \alpha can be determined from \cos \theta^* because

dN/d(\cos \theta^*) = 1 + \alpha (\cos \theta^*)^2.

All the above is to just say that one just needs to measure the angle of the positive muon from the Y direction, and then a few tricks allow the extraction of a measure of how many Y are polarized each way.

Experimentally, after the number of candidates in each bin is known, one uses Monte Carlo signal simulations with different input values of the parameter \alpha to find the one which matches the \cos \theta^* distribution better, for each P_T interval. The result is a determination of alpha as a function of P_T, which can be compared to theoretical expectations of NRQCD and to previous measurements by CDF. You can see the results for the Y(1S) meson below.

This result is quite striking! Not only does the D0 measurement (black points) show a very sharp variation of \alpha with the particle momentum, which is totally inconsistent with the predictions of NRQCD (yellow band). The D0 data points are also quite far away from what CDF found in a previous analysis (green points lining at \alpha close to zero).

A less conclusive result is found for Y(2S) mesons. For them, the statistical errors in \alpha are larger, and NRQCD remains a reasonable interpretation of the momentum trend.

I think the D0 measurement is sufficiently precise to throw the ball in the theoreticians’ court, where it is bound to stay long enough for a better description of Y polarization to become available. CDF is also bound to improve the precision of their own polarization measurement. We have the data, and the means: The mass resolution is much better than that of D0, so the number of candidates is much easier to extract… The challenge is on!

You can find more details on the D0 measurement of Upsilon polarization in the public page of their B physics analyses.

Update: Kea also discusses this result.



1. Karl - August 6, 2007

The images aren’t showing again. This time I looked at the page source, and it claims that the URL for one of the images is:


if I try just http://www.pd.infn.it (not itt) etc, I can see the image fine. Where’s the rest of the junk coming from?

Anyway, interesting post!

2. dorigo - August 6, 2007

Hi Karl,

I suspect it is a problem when posting from a slow connection such as the one I am using now, from vacations. For some reason wordpress converts the link using some strange alchemy. It works for me, but it indeed seems a wrong script. If I fix it it comes back the same… I think I will write to the admins about it.


3. jpivarski - August 6, 2007

Very interesting! I discovered your blog via the WordPress login page— I just had to read this article because I did my thesis on narrow Upsilon studies at CLEO. I measured the electron decay widths for a high-precision comparison with NRQCD, but never heard if the theorists completed this calculation (\Gamma_{ee}). Do you have pointers to the conferences where recent NRQCD results are being presented?

In my e+e- experience, this alpha is very precisely 1.0— the angular distribution is 1+(cosTheta)^2— because the Upsilon is a vector. (I must have looked at that plot hundreds of times!) I assume the polarization you’re talking about has something to do with Upsilon production in p-pbar collisions?

— Jim

4. Kea - August 7, 2007

OK, coooool. But I’m confused about the discrepancy with the CDF results, and I’d like some idea of exactly what was done differently.

5. Kea - August 7, 2007

OK, so to assume some analogy with the MiniBooNE/LSND discrepancy, which may be explained away by surmising (as Pitkanen did) an energy dependence to neutrino mass….

p here is just a transverse component, yeah? Was the D0 experiment somehow ‘more’ non-relativistic (low total E) than the CDF one? At a first guess, this seems like the most likely way to pick up true post-QCD effects.

6. dorigo - August 7, 2007

Hello j,

Yes, the Y polarization is complicated by the mix of different production mechanisms – something not completely understood yet, and in fact parametrized by universal long-distance matrix elements – a way to hide our ignorance of the details. Factorization of the different energy scales at play (M at quark production and vM at binding or decay) holds, but the polarization prediction seems off the data.

I will see if I find something new about NRQCD around, but am not at work and so my reaction time is slow these days.


7. dorigo - August 7, 2007

Hi Kea,

in fact I did a poor job in describing the plot above. The CDF measurements are the green points with error bars, which line up at alpha close to zero. I think the CDF analysis is easier to perform, because we have a much better resolution in muon momentum (and therefore narrower mass peaks, much easier to separate than in D0 – also check the first picture above). But ultimately, the alpha measurement is done by comparing with Monte Carlo and something can go wrong there too. I do think the D0 measurement is accurate though, and so the result is really intriguing.

About the energy dependence: CDF and D0 have the same center of mass energy for proton collisions. Heck, they stop short of using the very same protons (which unfortunately are removed from the beam when they collide). But D0 measures Y mesons up to larger rapidities (and thus higher P for given P_T) because their muon chambers cover further away from the interaction point along the beam direction. If things are done correctly, the acceptance is modeled by Monte Carlo, and the difference should not have an impact on the measured polarization asymmetry. However, the devil is indeed in the details. IF – big one – the parton distribution functions used by one of the experiments (or both) to model Y production in the Monte Carlos is screwed up somehow, or IF there really is a peculiarity in the high-rapidity production of Y states (indeed, when producing light things going forwards one is testing very low values of Bjorken x, where uncertainties are quite large), then the two experiments are measuring the same thing using data taken in two different regimes, to some extent, and there may lie the source of the discrepancy. Ultimately, if the data disagrees, one of the sets of data points has a systematic error unaccounted for. The two IFs above are suggestions of where these may come from.


8. Kea - August 8, 2007

OK, thanks a lot.

9. carlbrannen - August 8, 2007

This is all very interesting, but for me, none of the pictures show up. And I have a very high bandwidth connection.

10. Jimbo - August 8, 2007


The figures are missing…at least invisible on my screen.
What gives ?


11. dorigo - August 8, 2007

Hi all,

sorry to those of you who do not see the pictures. I think it has to do with a glitch of the editing window of wordpress, which does not load properly when I use a low bandwidth connection to write my posts.

I am unable to fix the problem now, but will do so upon getting back to work, a couple of weeks from now. Until then, you can still download the pictures if you look at the post page source, and typing the name of jpg or gif files after “http://www.pd.infn.it/~dorigo/”

Cheers all,

12. apetrov - August 11, 2007

Hi Tommaso,

Jonas Rademacker gave an excellent talk about that at CHARM 2007 (for his slides see here: http://www.lepp.cornell.edu/charm07/talks/Sunday/1110_rademacker.pdf) , especially pages 23, 24, 26, 27. He also has charmonium results there.

The physics of why Upsilon should be transversely polarized in NRQCD is easy: at high pT the main production mechanism for heavy onium is gluon fragmentation. That means that onium should retain gluon polarization, which, since gluon is massless, is transverse.

This assumes that unpolarizing interactions (soft gluon emissions) scale as at least one more power of velocity of b-quark inside the upsilon, which is quite small.

BTW, polarization measurements for J/psi are contaminated by J/psi’s produced in the decays of higher spin states (\chi’s, etc), which don’t give you transverse polarization. Why is the situation different for Upsilon (1s)? Upsilon(2s) results are consistent with NRQCD (so far)…



13. dorigo - August 12, 2007

Hi Alexey,

thank you for the talk pointer. And for the explanation of why NRQCD fails with alpha. As for studying Y(1S) and Y(2S) and the feed-down of the latter into the former: I think the sample of Y(1S) is indeed contaminated but the effect is not large. The 2S are consistent with NRQCD only because their statistics is poor and the fit has large uncertainties… If you look at the figure of the peaks extraction you will see why. I think CDF has the potential of doing much better here, we will soon see.


14. Not Even Wrong » Blog Archive » Various Stuff - September 15, 2007

[…] excellent detailed postings about recent experimental HEP results from Tommaso Dorigo, see here and here. For blogging from CHARM 07 by Alexey Petrov, see […]

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